None.
Not applicable.
1. Field of the Invention
The preferred embodiments of the present invention are directed generally to downhole logging tools and logs created with the tools. More particular, the preferred embodiments are directed to logging-while-drilling (LWD) resistivity tools and logs created with the resistivity tools. More particularly still, the preferred embodiments of the present invention are directed to determining fixed depths of investigation for LWD tools having multiple spaced transmitters and receivers and using multiple frequencies.
2. Background of the Invention
In the days before logging-while-drilling (LWD) tools, information regarding downhole formations was gathered using wireline logging tools. One such wireline logging tool is a resistivity tool for determining resistivity of the downhole formation. Resistivity is generally determined at several depths of investigation, where the depths of investigation in a conventional wireline tool operating at a low frequency (near 20 kilo-hertz) are a function of the spacing between each transmitter and a receiver or receiver pair. Thus, to obtain multiple depths of investigation in a wireline tool, multiple transmitters are mounted on the wireline device at spaced-apart locations from the receivers. FIG. 1 illustrates an array induction tool with multiple transmitter-receiver spacings. Software focusing techniques are then used to obtain fixed multiple depths of investigation, which techniques are based largely upon an assumption of linearity between conductivity of formation and tool response. Having resistivity measurements at fixed multiple depths of investigation aids geologists in determining important downhole characteristics such as the diameter of the invasion of the drilling mud into the formation, and the corresponding resistivities at various depths into the formation.
As technology has advanced in the exploration and recovery of hydrocarbons, it is now common to include an LWD tool, capable of performing resistivity measurements, as part of the bottomhole assembly (BHA) of a drillstring. LWD resistivity tools have many similarities with their wireline counterparts, which may comprise multiple transmitters spaced apart from a receiver pair, use of electromagnetic wave propagation, and creation of logs of resistivity. However, because of the differences in physical requirements between wireline and LWD tools, the frequency of operation of an LWD tool is typically different than that of a wireline tool. For example, many LWD tools operate at a frequency of 2 megahertz. It has been discovered in the prior art that the depth of investigation of a resistivity tool is also a function of frequency when higher frequencies are used. Thus, a wireline tool and an LWD tool having the same spacing between the transmitters and receiver, because of the differences in frequency, may have different depths of investigation.
There are circumstances, however, where geologists need to compare the measured resistivities as between LWD and wireline devices. For example, a geologist may need to make this comparison when assessing the volume of hydrocarbons remaining in a reservoir. However, comparing the results of an LWD resistivity log performed during drilling, having a first set of depths of investigation, and the results of a wireline log run many months or years thereafter, having a different set of depths of investigation, is difficult. That is to say, it is difficult to compare the results of the logs performed by the two different devices because their depths of investigation are different.
In the prior art, there have been attempts to mathematically modify logs gathered by LWD tools to match the depths of investigation of wireline devices. A paper titled xe2x80x9cMulti-Parameter Propagation Resistivity Interpretation,xe2x80x9d by W. Hal Meyer, presented at the Thirty-Eighth Annual Logging Symposium of the SPWLA, Jun. 15-18, 1997, discusses one such attempt. The Meyer paper and its cited references, teach a technique where the fixed depth of investigation curves are obtained by a linear combination of many raw corrected curves. These fixed depth of investigation curves have the desired radial response functions with fixed depths of investigation that are chosen to be close to those used in induction logging. Each desired response function, denoted as target response function, is produced by a linear combination of elemental response functions of the corrected curves (corrected for shoulder bed effect) of each transmitter-receiver spacing. A set of combination coefficients is then used to combine the corrected data to obtain fixed depth of investigation curves. These coefficients vary with formation resistivity. Meyer teaches calculating the coefficients for a number of discrete selected resistivities in advance, and the coefficients at actual formation resistivity are obtained by interpolation. In Meyer""s paper, each response of each receiver/transmitter spacing, which corresponds to specific transmitter-receiver spacing, is calculated by assuming a very thin cylindrical annulus, or invaded zone, around the tool with a resistivity slightly different from the homogeneous background. The difference between this calculated result and the background response of a homogeneous formation is plotted as a function of radial distancexe2x80x94a radial response function. The resulting curve is normalized so that the area under the curve is 1.0, as illustrated by FIG. 3. The depth of investigation (DOI) is defined to be the point which corresponds to one half of the area of the radial response function, also referred to as 50% point. FIG. 2 illustrates radial impulse response functions of an LWD resistivity tool in a 1.0 ohm-m formation. These response functions are obtained by assuming an annulus or invaded zone with xe2x80x9cslightly differentxe2x80x9d resistivity of 0.98 ohm-m, which is the method of Meyer and the prior art.
However, the inventors of the present specification have found that the radial response function calculation of the prior art is only valid when assuming small resistivity differences in the annulus. In the real setting, invaded zone resistivity can be much bigger, or smaller, than the formation resistivity. Under this situation, the nonlinear nature of the LWD resistivity tool response becomes more pronounced. More specifically, the radial response functions change not only with formation background resistivity but also with formation to invaded zone resistivity contrast. For high contrast formation, e.g. 1:10 to 1:100 or more, the response functions calculated using techniques such as Meyer are no longer valid. Therefore, the fixed depth of investigation curves based on these functions are prone to error.
Thus, what is needed in the art is a method that can accurately produce fixed depth of investigation curves regardless of formation resistivity contrast.
The problems noted above are solved in large part by a logging while drilling (LWD) tool that operates under the realization that the depth of investigation in high frequency electromagnetic resistivity tools is affected not only by the frequency of the electromagnetic wave used and the transmitter-to-receiver spacings, but also by the resistivity of the formation, and the resistivity contrast between the invaded zone and formation. More particularly, the specification discloses an electromagnetic resistivity LWD tool preferably having five transmitting antennas spaced apart from each other and from a set of two receiving antennas. Each of the transmitters operates at three distinct frequencies: 2 megahertz, 500 kilohertz, and 250 kilohertz. Thus, the preferred embodiments of the present invention are capable of measuring resistivity of a formation at several different frequencies, and at several different depths of investigation based in part on the transmitter-to-receiver spacing. Using the logs obtained, the formation resistivity and the invaded zone resistivity are determined by inversion techniques. The determined invaded zone and formation resistivity values are used when modeling responses of the tool, rather than mere small difference assumption used in the prior art.
With regard to determining or creating logs of resistivity at fixed depths of investigation different than those realized because of the physical parameters of the tool and the formation, the preferred embodiments perform a least-squares curve fitting algorithm to determine a function that models the relationship between the physical spacing of the transmitter-to-receiver pairs and the depths of investigation. The preferred embodiments also use a least-squares curve fitting algorithm to determine a function that models the relationship between the transmitter-to-receiver spacing and the measured resistivity. In order to convert the realized depths of investigation to other fixed depths of investigation, such as to match those of a wireline tool, the preferred embodiments utilize the function that describes the relationship between the physical spacing and the depths of investigation to determine a fictional physical spacing that, if used, would generate the depths of investigation desired. Once the physical spacing for the desired fixed depth of investigation is determined, the fictional physical spacing is used with the function that relates the physical spacing to measured resistivity to obtain a resistivity reading at the desired fixed depth of investigation.
Thus, the disclosed structure and methods comprise a combination of features and advantages which enable them to overcome the deficiencies of the prior art devices. In particular, the preferred embodiments describe a structure and related method for creating electromagnetic resistivity logs at fixed depths of investigation different than those actually realized by the electromagnetic resistivity tool, and which account for resistivities of the formation and are accurate in high contrast formations. The various characteristics described, as well as other features, will be readily apparent to those skilled in the art upon reading the following detailed description, and by referring to the accompanying drawings.